On the theory of the oscillatory integral operators and its applications to the Feyman path integral for the field theory

申请人成功地给出了描述相对论中量子粒子的狄拉克方程解的费曼路径积分的表达式。在更一般的情况下，给出了包括狄拉克方程在内的更一般方程的解的费曼路径积分的表达式。这个表达式以满足叠加原理的所有可能路径的概率振幅的“和”的形式给出，这些路径在任何方向上以任何速度向前和向后。在时间上向后移动的电子被解释为在时间上向前移动的正电子。这个表达式使我们能够直观地理解相对论性量子力学，并期望我们可以用比目前主要使用的摄动方法更直接的方法来构造相对论性量子电动力学。狄拉克方程的费曼路径积分已经有60多年没有给出了。

The applicant succeeded in giving the expression of the Feynman path integral for the solutions of the Dirac equations, which describe the quantum particles in the relativistic theory. In more general, the expression of the Feynman path integral was given for the solutions of more general equations including the Dirac ones.This expression is given in the form of the "sum" of the probability amplitude satisfying the superposition principle over all possible paths that go in any direction at any speed forward and backward in time. The electrons that go backward in time are interpreted as positrons that go forward in time. This expression enables us to understand the relativistic quantum mechanics intuitively and to expect that we can construct the relativistic quantum electrodynamics in terms of a more direct method than the perturbative one used mainly in the present. The Feynman path integral for the Dirac equations has not been given for 60 years or more.